Question

What is the derivative of `f(x)=cos^3x`?

Answer 1

`f'(x)=-3sinxcos^2x`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"Given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`f(x)=cos^3x=(cosx)^3`

`rArrf'(x)=3(cosx)^2xxd/dx(cosx)`

`color(white)(rArrf'(x))=3cos^2x xx-sinx`

`color(white)(rArrf'(x))=-3sinxcos^2x`